Education to Prepare for the Future
The promise of the American K-12 educational system is to develop strong numerically and scientifically literate critical thinkers who are ready for college and career in today’s Information Age. –U.S. Department of Education, 2019
This pledge is grounded in the understanding that children and adolescents, just like adults, must reason through a perpetual tidal wave of information, washing over them in school and beyond, through television, social media, and the Internet. Achievement of this ambitious educational goal requires the cultivation of critical literacies.
These include higher order thinking, scientific reasoning, information literacy, and numeracy. Research shows that mathematical reasoning, or numeracy, is as strong a predictor of students’ school success as reading ability.1 And, that the development of early mathematical skills and literacy skills is highly interrelated.2 Wiest offers a stronger perspective suggesting that quantitative literacy is, in essence, a gatekeeper for effective functioning today.3
The development of quantitative literacy in all children is a matter of social justice in the 4th Industrial Revolution.
In this era of Common Core State Standards, where depth of understanding, critical thinking, and real-world problem solving receive heightened attention as learning outcomes, educators are emphasizing problem-based learning. This transition in practice is meant to provide creative learning opportunities for all students.4
Similarly, the scholarly community must critically evaluate the impacts of an enriched thinking and problem-solving focused pedagogical approach to elementary and secondary education. Rigorous educational research into the characteristics, variations, and developmental trajectories of children’s and adolescents’ critical thinking is of utmost importance.
This information is needed by our children’s teachers as they strive to nurture critical thinking in tomorrow’s citizens and leaders.
Predicting early middle school mathematics achievement
Critical thinking skill in early middle school (6th grade) has been found to be highly predictive of student mathematics achievement in later grades.5 In this three-year longitudinal study of students in California, scores on the EI Skills measure were strongly positive and significantly (p<.001) correlated with students’ math scores on the California Standardized Testing and Reporting (STAR) assessment program. In the first year of testing (6th grade), the correlation between students’ EDUCATE INSIGHT Skills and the California Standardized Test – Math (CST Math) overall scores was .635 (subscale correlations = .448-.601).
This tells us that approximately 40% of the variance in 6th grade students’ mathematics achievement, as measured by State mandated standardized test, could be predicted by these students’ 6th grade EDUCATE INSIGHT Overall critical thinking skills scores–a very strongly predictive finding.
When retested with EDUCATE INSIGHT Skills in 7th and 8th grade, strong and significant correlations with the CST Math persisted. There was also an observable relationship between these scores and whether teachers recommended students to advance to Algebra as 8th graders.
In this study, critical thinking skills in 6th grade powerfully predicted math course placement at 8th grade. But, more importantly, this demonstrated relationship between critical thinking and mathematics achievement in early middle school means that an assessment of critical thinking skills can identify students whose critical thinking skills need to be improved (to support their future learning in mathematics).
Can middle school students improve their critical thinking skills?
Evidence from another study, is more than reassuring. This evidence, gathered from struggling schools across the US, suggests that training critical thinking skills should be a fundamental focus of middle school.
The figure illustrates the difference scores for EDUCATE INSIGHT Skills in a sample of 422 middle school students, most of which are demonstrating benefit from a grant funded educational enrichment program. Not all children in this educational program are demonstrating gains. Some may be failing to fully engage a retest that challenges them to analyze, evaluate, and explain why. But the students represented by the solid black bars are demonstrating gains in critical thinking skills that correspond to significantly improved performance, when compared to the national distribution of critical thinking skills scores for children in these grade levels.
When is the right time to assess and train critical thinking?
How early is too early to assess and train critical thinking? In our view, it is never too early to empower children with better thinking skills. And, with careful attention to their ability to participate in an assessment process, it is possible to capture valid and reliable data about their thinking skills.
The EDUCATE INSIGHT series equips educators and researchers with tools to directly measure critical thinking among students as young as kindergarten. The conventional approach has been to indirectly approximate reasoning ability using standardized measures of student achievement, typically administered at the state level. Those assessments of students’ achievement are not routinely administered before 3rd grade. International exams such as the NAEP and TIMMS are not administered younger than 4th grade.
What have we learned so far about critical thinking at the K-2 level?
The EDUCATE INSIGHT Skills K-2 was administered to a sample of 100, male and female, first and second graders from an economically and ethnically diverse public-school district in the southern region of California’s Bay Area. The instrument was read aloud as students followed along. The next figure shows the distribution of the children’s Overall critical thinking scores. These young students’ scores array in a relatively normally distribution, the average score falling within the same value range as is observed with older students.
The reasoning skills tests grades 3 and higher include a numeracy metric. Numeracy, defined by Gittens as critical thinking in a quantitative context,6 emphasizes the use of analysis, inference, interpretation, explanation, evaluation, as well as reflection on one’s own reasoning process (metacognition and self-regulation). Much more than simply adding a column of numbers or solving for x, numeracy is the ability to set up the problem in the first place, that is determining which mathematical operations to apply, and in what order, so that one might reason correctly about the quantitative information available and resolve the question at hand.
There is great synergy between a focus on numeracy as critical thinking applied to the context of mathematics, probability and numerical data analysis and the overarching educational goal of building students’ critical thinking in both the K-12 and postsecondary levels.
Not surprisingly, the national standards reform movement in mathematics, as reflected by the Common Core State Standards Initiative (CCSI) draws heavily on the National Council of Teachers of Mathematics (NCTM) vision and recommendations and prioritizes numeracy.7 They emphasize number sense and problem solving, abstract and quantitative reasoning, argument construction and critique, structural analysis and strategic application of tools to solve math problems, and modeling with mathematics, as vital practice-based learning outcomes at all grade levels.8 In alignment with mathematics education, the centrality of quantitative reasoning and literacy manifesting in evidence-based explanations for science practice is emphasized in major science education documents including, the Next Generation Science Standards (NGSS).9
The Numeracy scale of the EDUCATE INSIGHT Reasoning Skills series provides a focused measure that is conceptually aligned with the reasoning and problem-solving skills endorsed by NCTM, NGSS, and reflected in the language of the Common Core Standards.
1 Perry, M. L. (2013). Strengthening early math: A high level strategy for meeting the Common Core challenge. San Jose, CA: Silicon Valley Education Foundation. Retrieved from https://svefoundation.org/wp-content/uploads/2016/10/Early-Math-SVEF-paper.pdf
2 Purpura, D. J., Logan, J. A. R., Hassinger-Das, B. & Napoli, A. R. (2017). Why do early mathematics skills predict later reading? The role of mathematical language. Developmental Psychology, 53, 1633-1642. DOI: http://dx.doi.org.libproxy.scu.edu/10.1037/dev0000375.
3 Wiest, L. R., H. J. Higgins, & J. H. Frost. (2007). Quantitative literacy for social justice. Equity & Excellence in Education, 40(1), 47–55.
4 Cash, J. (2013). Transitioning teaching and learning to embrace common core. Leadership, 43(2), 22-25. (Leadership is a publication of the Association of California School Administrators available to members. A contact point for the journal can be found at https://www.acsa.org/publications.)
5 Gittens, C. A. (2015). Assessing numeracy in the upper elementary and middle school years. Numeracy 8(1), Article 3. DOI: http://dx.doi.org/10.5038/`936-46188.8.131.52. Available at: http://scholarcommons.usf.edu/numeracy/vol8/iss1/art3
6 Gittens, 2015, op. cit.
7 National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics; National Council of the Teachers of Mathematics. (2006). Curriculum focal points for prekindergarten through grade 8: Mathematics a quest for coherence. Reston, VA: National Council of the teachers of Mathematics. National Council of the Teachers of Mathematics. (2009). Focus in high school mathematics: Reasoning and sense making. Reston, VA: National Council of the Teachers of Mathematics.
8 Burns, M. (2012). Go figure: Math and the Common Core. Educational Leadership, 70(4), 42–46. Common Core State Standards Initiative. (2019). Common Core Standards: Standards in your state. Retrieved from http://www.corestandards.org/standards-in-your-state/
9 NGSS Lead States. (2019). Next Generation Science Standards: For States, By States. Retrieved from https://www.nextgenscience.org/T